Pixel Club: Homotopic Morphing of Planar Curves

Nadav Dym (Weizmann Institute of Science)
Tuesday, 30.6.2015, 11:30
EE Meyer Building 1061

We present an algorithm for morphing between planar curves (with identical turning number), such that the morph is guaranteed to be a regular homotopy. This means that pinching will not occur in the intermediate curves, or in other words, global intersections are allowed but not local intersections. The algorithm is basically a modification of Sederberg's classical angle-length method necessary for providing the guaranteed regular homotopy. After presenting our results, we will discuss briefly the elegant theory of regular homotopy, and the theory behind our algorithm.

If time permits we will discuss how the algorithm can be adapted to morphing curves with different turning numbers. We will show that doing this correctly gives good results, with similar theoretical guarantees, but applying our method/angle-length directly will generally result in highly peculiar results.

Joint work with Anna Shtengel and Yaron Lipman.

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